Answer:
a) There is a 48% probability that both Alice and Betty watch TV tomorrow.
b) There is a 48% probability that Betty watches TV tomorrow.
c) There is a 12% probability that only Alice watches TV tomorrow.
Step-by-step explanation:
We have these following probabilities:
A 60% probability that Alice watches TV.
If Alice watches TV, an 80% probability Betty watches TV.
If Alice does not watch TV, a 0% probability that Betty watches TV, since she cannot turn the TV on by herself.
a) What is the probability that both Alice and Betty watch TV tomorrow?
Alice watches 60% of the time. Betty watches in 80% of the time Alice watches. So:
![P = 0.6*0.8 = 0.48](https://tex.z-dn.net/?f=P%20%3D%200.6%2A0.8%20%3D%200.48)
There is a 48% probability that both Alice and Betty watch TV tomorrow.
b) What is the probability that Betty watches TV tomorrow?
Since Betty only watches when Alice watches(80% of the time), this probability is the same as the probability of both of them watching. So
![P = 0.6*0.8 = 0.48](https://tex.z-dn.net/?f=P%20%3D%200.6%2A0.8%20%3D%200.48)
There is a 48% probability that Betty watches TV tomorrow.
c) What is the probability that only Alice watches TV tomorrow?
There is a 60% probability that Alice watches TV tomorrow. If she watches, there is an 80% probability that Betty watches and a 20% probability she does not watch.
So
![P = 0.6*0.2 = 0.12](https://tex.z-dn.net/?f=P%20%3D%200.6%2A0.2%20%3D%200.12)
There is a 12% probability that only Alice watches TV tomorrow.